Chapter 2 Measurements 2.7 Problem Solving Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Given and Needed Units To solve a problem: Identify the given unit Identify the needed unit Problem: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in)

Learning Check An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units in this problem. Given unit = _______ Needed unit = _______

Solution An injured person loses 0.30 pints of blood. How many milliliters of blood would that be? Identify the given and needed units in this problem Given unit = pints Needed unit = milliliters

Problem Setup Write the given and needed units. Write a unit plan to convert the given unit to the needed unit. Write equalities and conversion factors that connect the units. Use conversion factors to cancel the given unit and provide the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion = Needed unit factor unit

Guide to Problem Solving The steps in the guide to problem solving are useful in setting up a problem with conversion factors.

Setting Up a Problem How many minutes are 2.5 hours? Given unit = 2.5 hr Needed unit = ? min Unit Plan = hr min Set up problem to cancel hours (hrs). Given Conversion Needed unit factor unit 2.5 hr x 60 min = 150 min (2 SF) 1 hr Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Learning Check A rattlesnake is 2.44 m long. How many centimeters long is the snake? 1) 2440 cm 2) 244 cm 3) 24.4 cm

Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? 2) 244 cm 2.44 m x 100 cm = 244 cm 1 m

Using Two or More Factors Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors are placed in the setup to cancel each preceding unit. Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2

Example: Problem Solving How many minutes are in 1.4 days? Given unit: 1.4 days Factor 1 Factor 2 Plan: days hr min Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103 min 1 day 1 hr 2 SF Exact Exact = 2 SF

Check the Unit Cancellation Be sure to check your unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day2/min is Not the unit needed Units don’t cancel properly.

Using the GPS What is 165 lb in kg? STEP 1 Given: 165 lb Need: kg STEP 2 Plan STEP 3 Equalities/Factors 1 kg = 2.205 lb 2.205 lb and 1 kg 1 kg 2.205 lb STEP 4 Set Up Problem

Learning Check A bucket contains 4.65 L of water. How many gallons of water is that? Unit plan: L qt gallon Equalities: 1 L = 1.057 qt 1 gal = 4 qt Set Up Problem:

Solution Given: 4.65 L Needed: gallons Plan: L qt gal Equalities: 1 L = 1.057 qt 1 gal = 4 qt Set Up Problem: 4.65 L x 1.057 qt x 1 gal = 1.23 gal 1 L 4 qt 3 SF 4 SF exact 3 SF

Learning Check If a ski pole is 3.0 feet in length, how long is the ski pole in mm?

Solution 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm Calculator answer: 914.4 mm Needed answer: 910 mm (2 SF rounded) Check factor setup: Units cancel properly Check needed unit: mm

Learning Check If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet?

Solution Given: 7500 ft 65 m/min Need: min Plan: ft in cm m min Equalities: 1 ft = 12 in 1 in = 2.54 cm 1 m = 100 cm 1 min = 65 m (walking pace) Set Up Problem 7500 ft x 12 in x 2.54 cm x 1 m x 1 min 1 ft 1 in 100 cm 65 m = 35 min final answer (2 SF)

Percent Factor in a Problem If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg? percent factor 86 kg mass x 11 kg fat 100 kg mass = 9.5 kg fat Copyright © 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings

Learning Check How many pounds (lb) of sugar are in 120 g of candy if the candy is 25% (by mass) sugar?

Solution How many pounds (lb) of sugar are in 120 g of candy if the candy is 25%(by mass) sugar? % factor 120 g candy x 1 lb candy x 25 lb sugar 453.6 g candy 100 lb candy = 0.066 lb sugar